The morphodynamic equilibrium state of a river in backwater dominated reaches

When rivers are forced by statistically invariant boundary conditions (i.e. an upstream water discharge, upstream sediment discharge and downstream base level that fluctuate around constant mean values), and are not subject to any forcing with a temporal trend (e.g. no uplift/subsidence, no sea-level rise), they tend to a morphodynamic equilibrium state over time. Due to continuously changing boundary conditions a river may never reach its mean equilibrium state, yet it will tend to it continuously, and if the boundary conditions change at a sufficiently slow pace, the river may be in a quasiequilibrium state. Therefore, studying the equilibrium state of a river may help us to better understand the long-term trends that are observed in natural rivers, such as for instance the ongoing bed degradation in the Dutch Rhine. Available models used to predict the morphodynamic equilibrium state are mainly analytical ones that start from the assumption that there is always normal flow, during all stages of an imposed upstream hydrograph (Prins, 1969; Blom et al., in preparation). This means the hydrograph may include variable flow rates due to for instance flood waves, yet the hydrodynamic state of the river is modelled as a sequence of consecutive normal flow regimes. Variable flow rates, tidal forcing and spatial variations in, for instance, river width, however, can induce backwater effects, also in the equilibrium state. Here we propose an efficient model that describes the river’s behaviour also outside of the normal flow zone, in the so-called backwater segment (e.g. Nittrouer et al. 2012). The efficiency of this model results from the approach to solve for the equilibrium in a space-marching solution procedure (i.e. a backwater alike solution procedure), rather than using a time-marching model where long simulation times (e.g. 1000 years) are required before an equilibrium situation is reached.